WHAT CAN WE LEARN FROM COMPUTER SIMULATION? Ehud Raanani, MD Gil Marom, Phd Cardiothoracic Surgery, Sheba Medical Center Sackler School of Medicine, Biomechanical Engineering, Tel Aviv University Homburg, September 12, 2013 The Leviev Heart Center
Freedom from re-operation after 5 years (100PTS) 96.2% ± 2.6%
Freedom from 2+ AI 5 years 84% ± 6%
Courtesy; H.J Schafers Surgical Solutions Geometry altered by non-pressurized state! Stay sutures
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Geometric Relationships of the Aortic Root Kunzelman et. al. 1994
What are the normal diameters of the aortic root? Roman 1987 Kim 1996 Nistri 1999 Varnous 2003 Maselli 2005 Babaee 2007 Tamas 2007 Soncini 2009 Bierbach 2010 Zhu 2011 N 135 110 70 100 50 128 32 52 100 315 1132 Annular Ø STJ Ø STJ/ annulus 24.5 (± 3) 27.5 (± 3) 23.4 (± 2.4) 28.1 (± 3.2) 22.7 (± 2.7) 24.7 (± 2.8) 20.55 (± 3) 31.2 (± 3.7) 24.4 (± 4.1) 22.3±1,4 (20.5-32.4) 25.4 (± 4.1) 26.7±2.2 (31.2-23.4) 1.2±0.1 (1.1-1.3) 21.8±2.4 21± 3 21,6 21±2,8 20,3±8,7 29.5±3.1 27± 4 27,3 25± 3,7 23.4±3,1 1.12 1.2 1.1 1.3 1.1 1.3 1.3 1,3 1,2 1,1 Courtesy E Lansac
Annular and Sinuses Dilataion
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The numerical model: fluid structure interaction (FSI)
Nominal stress [kpa] The structure model (14,000 shell elements) The cusps: AV cusps consists of collagen fibers embedded in an elastin matrix Anisotropic and hyperelastic behavior Different layers of Collagen and Elastin (CFN) 10 regions with different fiber orientations and diameters 140 120 100 80 60 40 Collagen Elastin 20 0 0 0,1 0,2 0,3 Eng. Strain
Nominal stress [kpa] The Root Average behaviour of porcine aortic sinuses from Gundiah et al. (Ann. Thorac. Surg., 2008; J. Heart Valve Disease, 2008) Aortic root tissue assumed to be isotropic and hyperelastic 140 120 100 80 60 40 20 0 0 0,2 0,4 Eng. Strain
P [kpa] The flow model : Mesh ~700,000 Physiologic time dependent pressures were employed at the boundaries, representing pressures at the LV and the ascending aorta 15 12 LV Aorta Rigid wall Compliant aortic root Rigid wall 9 6 3 0-3 0 0,2 0,4 0,6 0,8 t [s] LV pressure left ventricle ascending aorta Aortic pressure
The non-pathologic FSI model
Parametric studies of aortic root geometry Influence of annulus diameter and cusp size Simplified linear elastic and isotropic model Solution duration of 10ms - constant BC Marom et al. (2012) J. Thorac. Cardiovasc. Surg. doi: 10.1016/j.jtcvs.2012.01.080 Marom et al. (2012) J. Thorac. Cardiovasc. Surg. doi: 10.1016/j.jtcvs.2012.08.043
Effect of annulus diameter Six geometries with different annulus diameters Calculated by expanding or shrinking the AA of normal case (24mm) The other dimensions were not changed 20mm 22mm 24mm 26mm 28mm 30mm C-C section
Effect of cusp size Five cases with different cusp size The root dimensions are identical to the 24mm case Geometric height 15.4mm 15.9mm 16.2mm 17.6mm 18.9mm Relative cusp size 86% 92% 100% 108% 116% C-C section h G
Influence of the geometry on coaptation 5 4 average h c [mm] 3 2 1 h C average h C [mm] 0 15 16 17 18 19 geometric height [mm] 3,5 3 2,5 2 1,5 1 0,5 0 20 22 24 26 28 30 AA diameter [mm]
Influence of the geometry on the max. σ max [kpa] principal stress The average dimensions case (h G =16.2mm, d AA =24mm) has the lowest mechanical stress 1000 900 800 700 600 500 400 300 200 100 0 15 16 17 18 19 geometrial height [mm] σ max [kpa] 900 800 700 600 500 400 300 200 100 0 20 22 24 26 28 30 AA diameter [mm] Maximum principal stress [kpa]
Coaptation vs. effective height Comparison of coaptation during diastole as a function of the effective height The effective height correlates well with valve coaptation The cusps in all the cases with h E <9mm prolapsed during 5 diastole h E h c [mm] 4,5 4 3,5 3 2,5 2 1,5 1 0,5 0 7 9 11 13 h E [mm] daa cusp area
Parametric studies of aortic root geometry The influence of graft size and STJ to AA ratio CFN model and hyperelastic material in the sinuses Time dependent and physiological BC
Dry parametric study Sixteen cases of aortic roots Were calculated from the base geometry with an applied outer pressure that expanded or shrank the initial AA and STJ
Stress distribution during diastole
Influence of d STJ /d AA on flow shear stress FSI parametric study with five cases of aortic roots Reducing d STJ /d AA increases the shear stress values To prevent AA expansion - valve-sparing with annuloplasty is preferable
Influence of asymmetry Effect of asymmetric BAV morphology on hemodynamics CFN model and hyperelastic material in the sinuses Time dependent and physiological BC
Effect of asymmetric BAV configuration Four morphologies of native AV: Tricuspid aortic valve (TAV) Asymmetric bicuspid aortic valve (BAV 1) with and without raphe Almost symmetric bicuspid aortic valve (BAV 2) TAV BAV 1 without raphe BAV 1 with raphe BAV 2
Stress during peak systole TAV has the largest opening area Highest stress values are found in BAVs with fused cusps Raphe region increases stress magnitudes The collagen fibers have higher stresses than the surrounding tissues BAV no. 2 has the lowest stress distribution but also very small opening area Max. principal stress [kpa] A TAV BAV no. 2 A BAV no.1 without raphe BAV no.1 with raphe
Velocity vectors and streamlines TAV BAV no. 1 without raphe Flow velocity magnitude [m/s] BAV no. 1 with raphe BAV no. 2
Flow shear stress during peak systole Higher systolic flow shear stresses are found on the cusps of BAVs The TAV model has the lowest shear stress, specifically on the coapting regions Flow shear stress [Pa] TAV BAV no. 2 BAV no.1 without raphe BAV no.1 with raphe
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Annuloplasty or Sub-comissural plication?
Summary of parametric studies: There is a normal or perfect symmetric case, that has the best combination of large coaptation, low diastolic tissue stress and low systolic flow shear stress Larger annulus and short cusps length results in higher tissue stress and less cusps coaptation Effective height measure correlates well with cusps coaptation Low STJ/annulus diameter results in high cusp tissue stress, annuloplasty should always be considered BAV have significant lower EOA Asymmetry of BAVs cause larger vortices near the cusps and higher flow shear stress on their tissue
Near Future?
Preservation of symmetric cusps 38 Geometric height (cusp length from nadir to free margin)
Thank you The Leviev Heart Center
Acknowledgments Gil Marom PhD Department of Biomechanical engineering, TAU Advisors: Prof. Moshe Rosenfeld Prof. Rami Haj-Ali Prof. Ehud Raanani Collaborators: Prof. Hans-Joachim Schäfers Prof. Hee-Sun Kim Dr. Sagit Ben Zekry Dr. Ashraf Hamdan Mechanics of composite materials lab members: Rotem Halevi Mor Peleg Support: Nicholas and Elizabeth Slezak Super Center for Cardiac Research and Biomedical Engineering at Tel Aviv University
Hammermeister et al, JACC 2000
Patients and methods From January 2001 to November 2009 305 patients underwent aortic valve preservation surgery (include dissections) 100 elective patients with AI greater than 2+ were includedluded
Dysfunction of Aortic Root
Aortic Cusps
Objectives To develop a compliant FSI model with: Coaptation between the cusps of the valve Physiologic material properties and realistic BC Mesh refinement study To determine the influence of modeling simplifications FSI with rigid root, dry model Parametric studies of aortic root geometry Annulus diameter, cusp size, STJ to annulus ratio To find the influence of BAVs on hemodynamics To model the effect of asymmetric porcine-specific collagen fibers alignment
Previous FSI models of aortic valves Prosthetic mechanical valves - rigid cusps FSI models of flexible valves Arbitrary Lagrangian Eulerian (ALE) Eulerian approach 2D (Lai et al., 2002; Dumont et al., 2004) 3D (Sotiropoulos and Borazjani, 2009) (Van Loon, 2005; Morsi et al., 2007; Katayama et al., 2008) - coaptation was not modeled Fictitious domain (FD) (De Hart et al., 2003; Astorino et al., 2009) - unrealistic BC LS-Dyna (Nicosia et al., 2003; Weinberg and Mofrad, 2007; Carmody et al., 2006) - no coaptation, compressible flow, explicit solver Peskin s immersed boundary (IB) method (Griffith et al., 2009) - semi-rigid root, unrealistic material properties, cannot achieve numerically converged results.
Haj-Ali et al. (2012) J. Biomech. 45:2392-2397 Parametric 3D geometry Geometry based on parametric curves and average dimensions The cusps z=0 section: x l = r co cos θ 1 r fo r co sin θ 1 n y=0 section: z = h 1 + h 1 free edge: x = r f + r c cos θ 1 r f z = h f + r l h r c h f = h f cl The sinuses y l n r v x r v r fo y r c sin θ 1 m N z=0 section: r = r co + r s r co cos 3 2 θ y=0 section: circle arc
The numerical model: fluid structure interaction (FSI)
3D FSI model of native aortic valves with: Cusps Coaptation Physiologic blood pressure Compliant Aortic Root Realistic material properties (AV cusps)
Parametric studies of aortic root geometry Influence of cusp size and aortic annulus diameter Simplified linear elastic and isotropic model Solution duration of 10ms - constant BC Marom et al. (2012) J. Thorac. Cardiovasc. Surg. doi: 10.1016/j.jtcvs.2012.01.080 Marom et al. (2012) J. Thorac. Cardiovasc. Surg. doi: 10.1016/j.jtcvs.2012.08.043
The structure model Implicit dynamic analysis Collagen Fiber Network (CFN) model Contact algorithm ~14,000 Shell elements Abaqus (Simulia)
P [kpa] The flow model 15 12 9 6 3 0-3 Eulerian method + mesh adaptation Laminar flow ~700,000 elements FlowVision HPC (Capvidia) LV Aorta 0 0,2 0,4 0,6 0,8 t [s] LV pressure Rigid wall left ventricle Compliant aortic root Rigid wall ascending aorta Aortic pressure
Nominal stress [kpa] The structure model the cusp Radial stress-strain from Mavrilas & Missirlis (1978) 10 regions with different fiber orientations and diameters 140 120 100 80 60 40 Collagen Elastin 20 0 0 0,1 0,2 0,3 Eng. Strain
Nominal stress [kpa] The structure model the root Average behaviour of porcine aortic sinuses from Gundiah et al. (Ann. Thorac. Surg., 2008; J. Heart Valve Disease, 2008) 140 120 100 80 60 40 20 0 0 0,2 0,4 Eng. Strain
70 160 220 270 60 30 0 100 50 0 The non-pathologic FSI model (cont.) 30 Pressure [mmhg] Stress [KPa] 70 160 220 120 90 60 30 0 200 150 100 50 0 30 70 160 220 270 90 60 30 0 200 150 100 50 0 [ms] 30 Pressure [mmhg] Max. Principal Stress [KPa] 70 160 220 120 90 60 30 0 200 150 100 50 0 Hemodynamics Tissue mechanics Pressure [mmhg] Max. Principal Stress [KPa] 120 90 60 30 0 200 150 100 50 0 t [ms] Hemodynamics Tissue me 30 Pressure [mmhg] Max. Principal Stress [KPa] 70 160 220 120 90 60 30 0 200 150 100 50 0 t [ms] Hemodynamics Tissue mechanics 30 Pressure [mmhg] Max. Principal Stress [KPa] 70 160 220 120 90 60 30 0 200 150 100 50 0
Model verification and comparison with simplified model Simplified linear elastic and isotropic model Solution duration of 10ms - constant BC Marom et al. (2012) Med. Biol. Eng. Comput. 50:173-182, doi: 10.1007/s11517-011-0849-5
Verification of the model - mesh Refinement studies of the structure and flow meshes The solution is independent on the mesh Flow Structure 700,000 elements 14,000 elements 0 0-0.2-0.2-0.4-0.4 w z / w r [mm] -0.6-0.8-1 -1.2 w r 700,000 w z 700,000 w r 2,000,000 w z 2,000,000 w z / w r [mm] -0.6-0.8-1 -1.2 w r 14,300 w z 14,300 w r 125,000 w z 125,000-1.4 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 t [ms] -1.4 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 t [ms]
FSI model with compliant root t=0 t=2ms t=4ms t=6ms t=8ms 350 C Maximum principal stress [kpa] 250 150 50-50 C C-C section Pressure on LV side [mmhg] 80 60 40 Pressure on aorta side [mmhg] 20 0
Simplified models
Influence of asymmetry FSI model with porcine-specific collagen fibers alignment Native CFN model and hyperelastic material in the sinuses Time dependent and physiological BC
Native CFN model The network was mapped from digital microscope photos The CFN defined by: length, thickness, alignment Simplified CFN Symmetric circular arcs, identical for all three cusps The mapped collagen Left cusp Posterior cusp Right cusp Simplified CFN fiber network (CFN) Native cusps The mapped collagen fiber network (CFN) Simplified CFN
Asymmetric vs. symmetric valves
Asymmetric effect on the kinematics
Computer Finite Element Model, FSI
Summary 3D FSI model of native aortic valves with: Coaptation Compliant root Physiologic blood pressure Realistic material properties Dry vs. FSI models: larger displacement and stress values Parametric studies: the normal case has the best combination of large coaptation, low diastolic tissue stress and low systolic flow shear stress Asymmetry of BAVs cause larger vortices near the cusps and higher flow shear stress on their tissue Asymmetric fibers alignment: different stress distribution in each cusps and asymmetric hemodynamics